Electron. J. Differential Equations, Vol. 2016 (2016), No. 243, pp. 1-10.

Lyapunov-type inequalities for odd order linear differential equations

Sougata Dhar, Qingkai Kong

Abstract:
In this article, we obtain Lyapunov-type inequalities for certain odd order linear boundary-value problems. Our inequalities involve integrals of both $q_+(t)$ and $q_-(t)$ in addition to that of $|q(t)|$. The Green's function for even order boundary-value problems plays a key role in our proofs. Also, using the Fredholm alternative theorem, we obtain a criterion for the existence and uniqueness of solutions to the corresponding nonhomogeneous linear boundary-value problems.

Submitted July 7, 2015. Published September 7, 2016.
Math Subject Classifications: 34A40, 34B05, 34C11, 26D20.
Key Words: Lyapunov-type inequalities; odd order; linear differential equations; Green's function; boundary value problem.

Show me the PDF file (216 KB), TEX file for this article.

Sougata Dhar
Department of Mathematics
Northern Illinois University
DeKalb, IL 60115, USA
email: sdhar@niu.edu
Qingkai Kong
Department of Mathematics
Northern Illinois University
DeKalb, IL 60115, USA
email: qkong@niu.edu

Return to the EJDE web page